On methods to determine bounds on the Q-factor for a given directivity
Résumé
This paper revisit and extend the interesting case of bounds on the Q-factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between bandwidth and a desired directivity is still not fully understood, not even for small antennas. Initial investigations in this direction has related the radius of a circumscribing sphere to the directivity, and bounds on the Q-factor has also been derived for a partial directivity in a given direction. In this paper we derive lower bounds on the Q-factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semi-definite relaxation techniques (SDR). We also show that the relaxed solution is also a solution of the original problem of determining the lower Q-factor bound for a total desired directivity. SDR can also be used to relax a class of other interesting nonconvex constraints in antenna optimization such as tuning, losses, front-to-back ratio. We compare two different new methods to determine the lowest Q-factor for arbitrary shaped antennas for a given total directivity. We also compare our results with full EMsimulations of a parasitic element antenna with high directivity
Mots clés
arbitrary-shaped antennas
SDR techniques
Q-factor
Antenna Q
Bandwidth
Directive antennas
miniature antenna
antenna theory
convex problem
semidefinite relaxation
directional antennas
Convex functions
antenna radiation pattern
Optimization
convex programming
fundamental limitations
electromagnetic simulations
parasitic element antenna
antenna optimization
nonconvex constraints
impedance bandwidth
Antenna radiation patterns